Methods and apparatus for privacy preserving data mining using statistical condensing approach

ABSTRACT

Methods and apparatus for generating at least one output data set from at least one input data set for use in association with a data mining process are provided. First, data statistics are constructed from the at least one input data set. Then, an output data set is generated from the data statistics. The output data set differs from the input data set but maintains one or more correlations from within the input data set. The correlations may be the inherent correlations between different dimensions of a multidimensional input data set. A significant amount of information from the input data set may be hidden so that the privacy level of the data mining process may be increased.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application is a continuation of U.S. application Ser. No.10/641,935 filed on Aug. 14, 2003, the disclosure of which isincorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates generally to privacy preserving datamining and, more particularly, to condensing a multidimensional data setand preserving statistical information regarding the multidimensionaldata set in order to create an anonymized data set.

BACKGROUND OF THE INVENTION

Privacy preserving data mining has become important due to the largeamount of personal and consumer data tracked by automated systems on theInternet. The proliferation of electronic commerce on the World Wide Webhas resulted in the storage of large amounts of transactional andpersonal user information. In addition, advances in hardware technologyhave made it technologically and economically feasible to trackinformation about individuals from transactions in everyday life. Forexample, a simple transaction, such as using a credit card, results inautomated storage of information about a user's buying behavior. Theunderlying data may consist of demographic information and specifictransactions. It may not be desirable to share such informationpublicly, therefore, users are unwilling to provide personal informationunless the privacy of sensitive information is guaranteed. In order toensure effective data collection, it is important to design methodswhich can mine the necessary data with a guarantee of privacy.

The nature of privacy in the context of recent trends in informationtechnology has been a subject of note among many authors, see, e.g.,articles such as C. Clifton et al., “Security and Privacy Implicationsof Data Mining,” ACM SIGMOD Workshop on Research Issues in Data Miningand Knowledge Discovery, pp. 15-19, May 1996; L. F. Cranor, “SpecialIssue on Internet Privacy,” Communications of the ACM, 42(2), February1999; “The End of Privacy,” The Economist, May 1999; K. Thearling, “DataMining and Privacy; A Conflict in Making,” March 1998; “The Death ofPrivacy,” Time, August 1997; and J. M. Reagle Jr. et al., “P3P andPrivacy on the Web,” The World Wide Web Consortium,http://www.w3.org/P3P/P3FAQ.html, April 2000. This interest has resultedin a considerable amount of focus on privacy preserving data collectionand mining methods, see, e.g., articles such as D. Agrawal et al.,“Privacy Preserving Data Mining,” Proceedings of the ACM SIGMODConference, 2000; P. Benassi, “Truste: An Online Privacy Seal Program,”Communications of the ACM, 42(2):56-59, 1999; V. Estivill-Castro et al.,“Data Swapping: Balancing Privacy Against Precision in Mining for LogicRules,” Data Warehousing and Knowledge Discovery DaWak99, pp. 389-398;A. Evfimievski et al., “Privacy Preserving Mining of Association Rules,”ACM KDD Conference, 2002; C. K. Liew et al., “A Data Distortion byProbability Distribution,” ACM TOD, 10(3):395-411, 1985; T. Lau et al.“Privacy Interfaces for Information Management,” Communications of theACM, 42(10):88-94, October 1999; and J. Vaidya, “Privacy PreservingAssociation Rule Mining in Vertically Partitioned Data,” ACM KDDConference, 2002.

In order to preserve privacy in data mining operations a perturbationapproach has typically been utilized. This technique reconstructs datadistributions in order to perform the mining by adding noise to eachdimension, thus treating each dimension independently. Therefore, thetechnique ignores the correlations between the different dimensionsmaking it impossible to reconstruct the inter-attribute correlations inthe data set. In many cases, relevant information for data miningmethodologies, such as classification, is hidden in the inter-attributecorrelations, see, e.g., S. Murthy, “Automatic Construction of DecisionTrees from Data: A Multi-Disciplinary Survey,” Data Mining and KnowledgeDiscovery, pp. 345-389, 1998.

An existing data mining technique uses a distribution-based analog of asingle-attribute split methodology, (see, e.g., R. Agrawal et al.). Thistechnique does not use the multidimensional records, but uses aggregatedistributions of the data as input, leading to a fundamental redesign ofdata mining methodologies. Other techniques such as multi-variatedecision tree methodologies, (see, e.g., S. Murthy), cannot be modifiedto work with the perturbation approach due to the independent treatmentof the different attributes. Therefore, distribution based data miningmethodologies have an inherent disadvantage in the loss of implicitinformation available in multidimensional records. It is difficult toextend the technique to reconstruct multi-variate distributions, becausethe amount of data required to estimate multidimensional distributions(even without randomization) increases exponentially with datadimensionality, see, e.g., B. W. Silverman, “Density Estimation forStatistics and Data Analysis,” Chapman and Hall, 1986. This is often notfeasible in many practical problems because of the large number ofdimensions in the data.

Thus, a need exists for improved privacy preserving data miningtechniques, which overcome these and other limitations.

SUMMARY OF THE INVENTION

The present invention provides privacy preserving techniques for use inassociation with data mining processes.

For example, in one aspect of the invention, a technique for generatingat least one output data set from at least one input data for use inassociation with a data mining process comprises the following steps.First, data statistics are constructed from the at least one input dataset. Then, an output data set is generated from the data statistics,wherein the output data set differs from the input data set butmaintains one or more correlations from within the input data set.

Advantageously, the present invention may provide techniques for privacypreserving data mining of multidimensional data sets and, moreparticularly, for condensing the multidimensional data set andpreserving statistical information regarding the multidimensional datasets in order to create anonymized data sets.

Thus, the inventive technique may maintain correlations betweendifferent dimensions in the data set, allowing for a reconstruction ofthe inter-attribute correlations in the new anonymized data set.Therefore, implicit information remains available in the new anonymizeddata set.

Another advantageous property is that the privacy of the user may beenhanced by increasing the amount of masked information from the inputmultidimensional data set. A larger number of records may be condensedinto a single statistical group and an anonymized data set may begenerated from the single statistical group. At the same time, thecondensed statistical data can provide a higher classification accuracythan the original data because of the statistical removal of anomaliesfrom the original data set.

These and other objects, features, and advantages of the presentinvention will become apparent from the following detailed descriptionof illustrative embodiments thereof which is to be read in connectionwith the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram illustrating a hardware implementationsuitable for employing methodologies, according to an embodiment of thepresent invention;

FIG. 2 is a flow diagram illustrating a privacy preserving data miningmethodology, according to an embodiment of the present invention;

FIG. 3 is a flow diagram illustrating a data statistics creationmethodology for static data sets, according to an embodiment of thepresent invention;

FIG. 4 is a flow diagram illustrating a data statistics creationmethodology for dynamic data sets, according to an embodiment of thepresent invention; and

FIG. 5 is a flow diagram illustrating an anonymized data set creationmethodology, according to an embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The following description will illustrate the invention using anexemplary data processing system architecture. It should be understood,however, that the invention is not limited to use with any particularsystem architecture. The invention is instead more generally applicableto any data processing system in which it is desirable to performefficient and effective privacy preserving data mining.

As will be illustrated below, the present invention introducestechniques for privacy preserving data mining. A multidimensional dataset is condensed into statistical information which maintains theinherent correlations between the different dimensions of themultidimensional data set. An anonymized data set is then generated fromthese statistics, maintaining the inherent correlations but permitting asignificant amount of information to remain hidden so that the privacylevel is increased.

In accordance with the present invention, a methodology condenses inputdata sets into multiple groups having a predefined number of records.For each group, a certain level of statistical information about therecords is maintained. This statistical information preservescorrelations across the different dimensions. Within a group, it is notpossible to distinguish different records from one another. The minimumsize, k, of each group is referred to as the indistinguishabilityfactor. The larger the indistinguishability factor, the greater theamount of privacy. At the same time, a greater amount of information ishidden because of the condensation of a larger number of records into asingle statistical group.

Each group of records is referred to as a condensed group. G denotes acondensed group containing records X(1) . . . X(k). Each record X(i)contains dimensions d which are denoted by x_(i) ¹ . . x_(i) ^(d). Thefollowing information is maintained about each group of records:

For each attribute j, the sum of corresponding values is denoted by

$\sum\limits_{i = 1}^{k}{x_{i}^{j}.}$The corresponding first-order sums are denoted as Fs_(j)(G), and thevector of first order sums is denoted as Fs(G).

For each pair of attributes i and j, the sum of the product ofcorresponding attribute values is denoted as

$\sum\limits_{i = 1}^{k}{x_{t}^{i} \cdot {x_{t}^{j}.}}$The corresponding second order sums are denoted as Sc_(ij)(G) and thevector of second order sums is denoted as Sc(G). The total number ofrecords k in that group is denoted as n(G).

Thus, the mean value of attribute j in group G is given by

${Fs}_{j}\frac{G}{n}{G.}$

The covariance between attributes i and j in group G is given by

${{Sc}_{ij}\frac{G}{n}G} - {{Fs}_{i}{G \cdot {Fs}_{j}}\frac{G}{n}{G^{2}.}}$

Group construction techniques differ depending upon whether an entiredata set of records is available, or whether the records arrive in anincremental fashion. Therefore, there are two approaches forconstruction of class statistics: (i) when the entire data set isavailable and individual subgroups need to be created from it; and (ii)when the data records need to be added incrementally to the individualsubgroups.

The methodology for creation of subgroups from the entire data set is astraightforward iterative approach. In each iteration, a record X issampled from data set D. The closest (k−1) records to this individualrecord X are added to this group. This group is denoted by G. Thestatistics of the k records in G are computed. Next, the k records in Gare deleted from data set D, and the process is repeated iteratively,until data set D is empty. At the end of the process, it is possiblethat between 1 and (k−1) records may remain. These records can be addedto their nearest subgroup in the data.

In accordance with the present invention, statistical information aboutthe data set D is represented in each group. This statisticalinformation can be used to create an anonymized data set, which hassimilar statistical characteristics to data set D. If desired, thetechnique discussed in this invention can also be extended to a dynamicsetting.

Referring initially to FIG. 1, a block diagram illustrates a hardwareimplementation suitable for employing methodologies, according to anembodiment of the present invention. As illustrated, an exemplary systemcomprises a user 10 interacting with a computer 20. Computer 20 maycomprise a central processing unit (CPU) 30 coupled to a data storagedevice 40 and a screen 50.

The data mining computations of the invention are performed at CPU 30 oncomputer 20 and sent to user 10. It is to be understood that, in thisillustrative embodiment, user 10 issues the requests for data mining andalso supplies the data sets to computer 20. Data storage device 40 isused to store some or all of the intermediate results performed duringthe computations. Results of these computations are then returned touser 10. It is assumed that the interaction between computer 20 and user10 may be an interactive process in which the user may repeatedlyspecify different data sets for the privacy preserving data miningtechnique.

In one preferred embodiment, software components including instructionsor code for performing the methodologies of the invention, as describedherein, may be stored in one or more memory devices described above withrespect to computer 20 and, when ready to be utilized, loaded in part orin whole and executed by CPU 30.

Referring now to FIG. 2, a flow diagram illustrates a privacy preservingdata mining methodology, according to an embodiment of the presentinvention. The approach utilizes two steps: (i) construction of thecondensed statistics from data set D; and (ii) generation of theanonymized data set from these condensed data statistics. Data set D isinput and the methodology begins at step 200. In step 210, the condenseddata statistics are constructed from data set D. This condensed data maybe generated either from static or dynamic data sets, as will beillustrated in the context of FIGS. 3 and 4, respectively. In staticdatabases, the entire data is available at the beginning of thecondensing step; while in dynamic data sets, records of a data set areavailable individually. In block 220, the anonymized data set isgenerated from the condensed data statistics. This step is described inmore detail in FIG. 5. The methodology terminates at step 230.

Referring now to FIG. 3, a flow diagram illustrates a data statisticscreation methodology for static data sets, according to an embodiment ofthe present invention. This figure can also be considered a detaileddescription of step 210 of FIG. 2 when the data sets available arestatic in nature. A static data set and indistinguishability factor kare input and the methodology begins at step 300. Step 310 finds a setof (k−1) records in the data set that are closest to a given datarecord. Any distance function which is known in the literature may beused in order to find the set of closest records, e.g., Euclideandistance measure. The selected data records and the given data recordare then deleted from the static data set in step 320. Step 330 thendetermines whether any records remain in the static data set. If recordsremain in the static data set, the methodology returns to step 310 toform an additional condensed data group. If no records remain in thestatic data set, the first order and second order statistics areconstructed for each group of records in step 340. The first orderstatistics of a group of records represent the sum of the records overeach dimension. The second order statistics of a group of recordsrepresent the sum of the squares of the records for each dimension. Inaddition, the number of points in each group are also included in thegroup statistics. The statistics for each group are then stored on diskin step 350 and the methodology terminates at step 360.

Referring now to FIG. 4, a flow diagram illustrates a data statisticcreation methodology for dynamic data sets, according to an embodimentof the present invention. This figure can also be considered a detaileddescription of step 210 of FIG. 2 when the data sets available aredynamic in nature. This methodology is achieved by receiving the recordsone by one and adding them to condensed data groups. The methodologybegins at step 400 where the dynamic data set and indistinguishabilityfactor k are input. In step 410, a record from data set D is received.The condensed group, having the closest records, is then found and therecord is added to the group in step 420. The first record receivedforms a first condensed group. The first order statistics and secondorder statistics are then constructed for the modified condensed datagroup in step 430. In step 440, it is determined whether the number ofrecords in the recently updated group is greater thanindistinguishability factor k. If the number of records is larger thank, the group is split into two smaller groups in step 450. In splittingthe group, the condensed data statistics for the two split groups isapproximately re-computed. In order to perform this computation, it isassumed that the data is distributed uniformly within each group. Theuniform distribution assumption provides reasonable solutions for smalldata localities. When a group is split, it is assumed that the variancealong the direction with the greatest data spread is reduced by aquarter. At the same time, it is assumed that the co-variances among therecords in the group remain the same. In step 460, it is determinedwhether all the records of the dynamic data set have been processed. Ifall the records have not been processed, the methodology returns to step410 in order to process the next record. If all the records have beenprocessed, the methodology terminates at step 470.

Referring now to FIG. 5, a flow diagram illustrates an anonymized datacreation methodology, according to an embodiment of the presentinvention. This figure can also be considered a detailed description ofstep 220 of FIG. 2. The methodology begins at step 500 where condensedstatistics are input. Step 510 generates the eigenvectors andeigenvalues for the co-variance matrix of each condensed data group, ora set of d-dimensional records. The co-variance matrix is defined as ad*d matrix, in which the entry (i,j) represents the co-variance betweenthe dimensions i and j. The generation of eigenvectors and eigenvaluesfor a given set of records is well known in the art, see, e.g., C.Aggarwal et al., “Finding Generalized Projected Clusters in HighDimensional Spaces,” ACM SIGMOD Conference Proceedings, 2000. Theseeigenvectors represent the directions of correlation in the data.Specifically, the eigenvectors represent directions such that the secondorder correlations along those directions are zero. The eigenvaluesrepresent the variances along those directions. The anonymized data isgenerated using the corresponding eigenvectors and eigenvalues in step520. Along each eigenvector, the methodology generates data points witha random generator using the variances corresponding to the eigenvalues.These data points are the anonymized data. For each group, the number ofrecords generated is the same as that used to create the condensedstatistical group. Thus, the overall distribution of the anonymized datais similar to the overall distribution of the original data withoutrevealing the individual records. Therefore, due to the similarity indistribution, many data mining algorithms can be applied to theanonymized data in lieu of the original data. However, advantageouslysince the data is anonymized, privacy is preserved. The methodologyterminates at step 530.

Accordingly, as described herein, the present invention providestechniques for regenerating multidimensional data records, withoutmodifying existing data mining methodologies to be used with theinventive technique. This is a clear advantage over techniques such asthe perturbation method in which a new data mining methodology needs tobe developed for each problem. For example, in the credit card examplediscussed above, the present invention allows the demographic andtransactional information to remain private by anonymizing the dataafter the collection process. The invention is not limited toanonymizing the data at this point, for example, it may take placeduring the collection process or the actual data mining process. Thetechnique is designed to preserve the inter-attribute correlations ofthe data. The technique effectively preserves the inter-attributecorrelations of the data set. At the same time, in many cases, thecondensed data may provide a higher classification accuracy than theoriginal data because of the removal of anomalies from the data set.

Although illustrative embodiments of the present invention have beendescribed herein with reference to the accompanying drawings, it is tobe understood that the invention is not limited to those preciseembodiments, and that various other changes and modifications may bemade by one skilled in the art without departing from the scope orspirit of the invention.

1. A method of processing an input data set for use in association witha data mining process, comprising the steps of: obtaining the input dataset, wherein the input data set comprises a plurality of records, one ormore of the records comprising data representing more than one datadimension; iteratively placing the records into one or more groups;iteratively generating data statistics for each of the one or moregroups as the records are placed into the one or more groups; generatingone or more output data sets corresponding to the one or more groupsbased on the data statistics iteratively generated for each of the oneor more groups, wherein a given one of the one or more output data setsdiffers from the input data set but maintains one or more correlationsfrom within the input data set and wherein the records represented bythe given one of the one or more output data sets are substantiallyindistinguishable from one another thereby providing privacy during thedata mining process; and storing the one or more output data sets in astorage device for use in the data mining process.
 2. The method ofclaim 1, wherein each of the output data sets is anonymized.
 3. Themethod of claim 1, wherein the one or more correlations are inherentcorrelations between different dimensions of the input data set.
 4. Themethod of claim 1, wherein the input data set is a static data set. 5.The method of claim 1, wherein the input data set is a dynamic data set.6. Apparatus for processing an input data set for use in associationwith a data mining process, the apparatus comprising: a memory; and atleast one processor coupled to the memory operative to: (i) obtain theinput data set, wherein the input data set comprises a plurality ofrecords, one or more of the records comprising data representing morethan one data dimension; (ii) iteratively place the records into one ormore groups; (iii) iteratively generate data statistics for each of theone or more groups as the records are placed into the one or moregroups; (iv) generate one or more output data sets corresponding to theone or more groups based on the data statistics iteratively generatedfor each of the one or more groups, wherein a given one of the one ormore output data sets differs from the input data set but maintains oneor more correlations from within the input data set and wherein therecords represented by the given one of the one or more output data setsare substantially indistinguishable from one another thereby providingprivacy during the data mining process; and (v) store the one or moreoutput data sets in a storage device for use in the data mining process.7. The apparatus of claim 6, wherein each of the output data sets isanonymized.
 8. The apparatus of claim 6, wherein the one or morecorrelations are inherent correlations between different dimensions ofthe input data set.
 9. The apparatus of claim 6, wherein the input dataset is a static data set.
 10. The apparatus of claim 6, wherein theinput data set is a dynamic data set.
 11. The method of claim 1, whereinthe larger the number of records in a given one of the one or moregroups, the greater the substantial indistinguishability of the recordsin the given group and thereby the greater the privacy provided duringthe data mining process.
 12. An article of manufacture for processing aninput data set for use in association with a data mining process, thearticle of manufacture comprising a computer readable storage mediumhaving tangibly embodied thereon computer readable program code which,when executed, causes a computer to: obtain the input data set, whereinthe input data set comprises a plurality of records, one or more of therecords comprising data representing more than one data dimension;iteratively place the records into one or more groups; iterativelygenerate data statistics for each of the one or more groups as therecords are placed into the one or more groups; generate one or moreoutput data sets corresponding to the one or more groups based on thedata statistics iteratively generated for each of the one or moregroups, wherein a given one of the one or more output data sets differsfrom the input data set but maintains one or more correlations fromwithin the input data set and wherein the records represented by thegiven one of the one or more output data sets are substantiallyindistinguishable from one another thereby providing privacy during thedata mining process; and store the one or more output data sets in astorage device for use in the data mining process.